Merian Yehya Ibramhim, 27, was imprisoned for not abiding by her father's religion, Islam.
She gave birth to a daughter Tuesday in prison, where her 20-month-old son is also with her.
Her husband, a U.S. citizen, is also a practicing Christian, and said he doesn't think his wife will renounce her faith.
"There is pressure on her from Muslim religious leaders that she should return to the faith," Daniel Wani told CNN. "She said, 'How can I return when I never was a Muslim? Yes, my father was a Muslim, but I was brought up by my mother.' "
"I know my wife. She's committed," he added. "Even last week, they brought in sheikhs and she told them, 'I'm pretty sure I'm not going to change my mind.' "
In Sudan, women who are nursing get a reprieve from the death penalty until the child has been weaned. Under Sharia law -- Islamic law practiced in Sudan -- authorities must wait two years after the birth of a child to execute the mother.